Stoichiometric Aquatic Food-Web Models Coupling Pelagic and Benthic Zones

Abstract

Modeling under the framework of ecological stoichiometry allows the investigation of the effects of food quality on food web population dynamics. In this study, we model how dynamics are affected with two separate free phosphate pools (Benthic and Pelagic) within a two producer and one consumer food web. In addition to this new model, we add light-dependent seasonality and temperature-dependent stoichiometry factors. The seasonality factor will turn the carrying capacity K into a function of time K(t) closely following the Seasonality-Lotka-Volterra model (SLKE) derived in (Asik, 2018). Furthermore, a novel approach of implementing temperature in the form of a modified Arrhenius equation is used to further refine the maximum ingestion rate (a) for the consumer. We will investigate a total of three models: +Base Stoichiometric Aquatic Food-Web Model Coupling Pelagic & Benthic Zones

+Light-Dependent Seasonality Stoichiometric Model Coupling Pelagic & Benthic Zones

+Temperature & Light-Dependent Seasonality Stoichiometric Model Coupling Pelagic & Benthic Zones

Stability analysis, Bifurcation analysis, and numerical simulations of the three models are performed. We identify ecological thresholds in the base model by analytically analyzing the boundary equilibrium. We found that Daphnia extinction occurs when light levels are high (Large K values). Furthermore, we identify the values for which equilibriums turn to periodic orbits. The light-seasonality model shows new dynamics. At very high light environments (high K) and low seasonality (low e), Daphnia completely dies off. There is producer and grazer coexistence at very low light environments (high K) and high seasonality (high e). The temperature-seasonality model further showed more new dynamics. Daphnia survives during years when temperature fluctuations are minimal. Daphnia becomes extinct during years when temperature fluctuations are extreme.